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Received: October 03, 2016; revised: April 06, 2017; accepted: May 31, 2017 This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the final Version of Record (VOR). This work is currently citable by using the Digital Object Identifier (DOI) given below. The final VoR will be published online in Early View as soon as possible and may be different to this Accepted Article as a result of editing. Readers should obtain the final VoR from the journal website shown below when it is published to ensure accuracy of information. The authors are responsible for the content of this Accepted Article. To be cited as: Chem. Eng. Technol. 10.1002/ceat.201600533 Link to final VoR: https://doi.org/10.1002/ceat.201600533 This article is protected by copyright. All rights reserved.

Modeling and optimization in membrane bioreactor and moving bed biofilm reactor-membrane bioreactor Juan Carlos Leyva-Díaz1,2, José Manuel Poyatos1,2* 1Department of Civil Engineering, University of Granada, 18071 Granada, Spain 2Institute for Water Research, University of Granada, 18071 Granada, Spain *Correspondence: José Manuel Poyatos (E-mail: [email protected]), Department of Civil Engineering, University of Granada, 18071 Granada, Spain

Abstract A membrane bioreactor and two hybrid moving bed biofilm reactor-membrane bioreactor systems were studied regarding the process modeling and operation optimization through different mathematical models for organic matter and nitrogen removal. A multiple linear regression method and a multivariable statistical analysis were applied. The process variables were hydraulic retention time, total biomass concentration, temperature, chemical oxygen demand of the influent and total nitrogen of the influent. In general, the values of coefficient of determination (R2) for the different model fittings were higher for the hybrid MBBR-MBR processes than those obtained for the MBR, probably due to the presence of suspended and attached biomass in the hybrid MBBR-MBR systems. Keywords: Membrane bioreactor, Microbial kinetics, Modeling, Moving bed biofilm reactor, Optimization.

1. Introduction Membrane bioreactor (MBR) and hybrid moving bed biofilm reactor-membrane bioreactor (hybrid MBBR-MBR) constitute some of the most advanced technologies concerning wastewater treatment used today [1-5], becoming an excellent alternative to the conventional activated sludge process [6-8]. These systems allow to comply with effluent limits and water quality guideline [3,9], showing important advantages [10-13].

Despite their growing implementation, to the best of our knowledge there has been limited research on MBR and hybrid MBBR-MBR systems concerning process modeling and operation optimization. In this regard, modeling and optimization are required to explore the fundamental processes that govern reactor behavior [3,14,15]. Thus, these tools could improve the basic activated sludge models through a more accurate characterization of the biological processes, and a more precise control and optimization of the operational parameters of the wastewater treatment plants (WWTPs) [16-18].

In light of this, modeling and optimization of biological wastewater treatment systems such as MBR and hybrid MBBR-MBR have to be focused on the removal processes of organic matter and nitrogen [14]. They constitute invaluable tools in terms of time and effort required to assess different


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alternatives for providing knowledge on underlying mechanisms affecting process performance and reducing energy operational costs [3,19].

Multiple linear regression method is a mathematical and statistical technique that can be used to model and analyze wastewater treatment processes regarding organic matter and nitrogen removal depending on several independent variables [20,21]. In this research, the independent operation variables were hydraulic retention time (HRT), total biomass concentration (XT), temperature (T), chemical oxygen demand of the influent (CODinfluent) and total nitrogen of the influent (TNinfluent). Furthermore, three models were proposed for the kinetic parameters, i.e. maximum specific growth rate (µm), substrate half-saturation coefficient (KS) and yield coefficient (Y), to assess the heterotrophic and autotrophic kinetic behavior based on a mass balance for substrate applied to a bioreactor. This experimental design is based on fitting the model by the least squares technique [22].

The increase of the efficiency of the processes of organic matter and nitrogen removal without increasing the cost is a fundamental method used to get a higher operation performance, which is called optimization. Optimization consists on choosing the values for independent variables to obtain the best system response from sets of available alternatives [23].

In light of this, the design procedure includes (i) the design of a series of experiments for measurement of the response of interest, (ii) the development of a mathematical-statistical model for the organic matter and nitrogen removal through the application of a multiple linear regression method and a multivariable statistical analysis, (iii) the obtention of the optimum experimental process variables that produce a maximum value of response, (iv) the development of mathematical models for the heterotrophic and autotrophic kinetic parameters, (v) the assessment of the optimum kinetic parameters by considering the optimum experimental process variables and the models proposed, and (vi) the evaluation of the substrate degradation rate for organic matter and nitrogen removal by applying the optimum kinetic parameters.

Thus, this methodology gives a systematic preview to achieve the optimum operation conditions for desirable responses regarding organic matter and nitrogen removal efficiency and kinetic performance as well as reducing the number of experimental runs in an effective manner [14].

In this study, chemical oxygen demand (COD) and total nitrogen (TN) removal as well as the heterotrophic and autotrophic kinetic parameters were assessed as a function of different operation variables such as HRT, XT, T, CODinfluent and TNinfluent in MBR and hybrid MBBR-MBR. The aim of this work was to develop mathematical models in terms of organic matter and nitrogen removal from municipal wastewater and kinetic performance to optimize the operation conditions.

2. Experimental

2.1. Description of the wastewater treatment plants The pilot-scale WWTPs, which were designed for organic matter and nitrogen removal, consisted of an MBR (Fig. S1a, Supporting Information), a hybrid MBBR-MBRa which had carriers in the anoxic and aerobic chambers of the bioreactor (Fig. S1b, Supporting Information), and a hybrid MBBR-MBRb which contained carriers only in the aerobic zone of the bioreactor (Fig. S1c, Supporting Information). The description of these WWTPs is given in Text S1 in the Supporting Information.

2.2. Operation conditions The variables analyzed in this study were the type of wastewater treatment plant (WWTP), HRT, XT in the bioreactor, as mixed liquor suspended solids (MLSS) for suspended biomass and/or biofilm density (BD) for attached biomass, T, CODinfluent and TNinfluent. TNinfluent was the sum of organic nitrogen, ammonium-nitrogen, nitrite-nitrogen and nitrate-nitrogen. These operational conditions



are shown in Tab. S1 in the Supporting Information. Operational conditions number 8 and 10 are not published, although the analysis was carried out globally. The value ranges of the operational conditions are specified in Text S2 in the Supporting Information.

The COD and TN removals and the kinetic parameters for heterotrophic and autotrophic biomass under the different operational conditions are indicated in Tab. S2 in the Supporting Information. In this regard, the following kinetic parameters were evaluated: maximum specific growth rate for heterotrophic biomass (μm,H), half-saturation coefficient for organic matter (KM), yield coefficient for heterotrophic biomass (YH), maximum specific growth rate for autotrophic biomass (μm,A), half-saturation coefficient for ammonia nitrogen (KNH), yield coefficient for autotrophic biomass (YA).

2.3. Statistical analysis A multivariable statistical analysis applying the software Canoco for Windows v. 4.5 (ScientiaPro, Budapest, Hungary) was used to quantify the influence of the environmental variables (HRT, XT, T, CODinfluent and TNinfluent) on the species data (COD and TN removal and the kinetic parameters for heterotrophic and autotrophic biomass), and to obtain the variables with the highest influence on the behavior of the different systems studied [24]. For this, the length and the angles between the different vectors symbolizing the variables and species were considered. This analysis is described in Text S3 in the Supporting Information.

2.4. Mathematical modeling and optimization In order to fit the functions that describe the removal of organic matter and total nitrogen, YOM and YTN, respectively, depending on the HRT, XT, T, and CODinfluent (for the organic matter removal) or TNinfluent (for the total nitrogen removal), a multiple linear regression method was used [21].

In light of this, the multiple linear regression method analyzes four independent variables (HRT, XT, T, and CODinfluent or TNinfluent) and another dependent one (YOM for organic matter removal or YTN for total nitrogen removal). For the formulation of this mathematical model regardless of the organic matter or TN removal, CODinfluent and TNinfluent are represented as So, and the response variable was named as YOM/TN.

YOM/TN can be expressed by a linear function of the variables HRT, XT, T and So through the coefficients β0,H/A, β1,H/A, β2,H/A, β3,H/A and β4,H/A, according to Eq. (1):

For that, a normal probability model is considered, as appears in Eq. (2):

The parameters β0,H/A, β1,H/A, β2,H/A, β3,H/A and β4,H/A set the values of the independent variables HRTi, XT,i, Ti and So,i and allow to obtain the corresponding values of YOM/TN,i, according to Eq. (3):

The matrix of random error U is determined as observed in Eq. (4):

β β β β β

β β β β β

β β β β β …

ϵ β β β β β σ …



Eqs. (5) and (6) represent the mathematical model as a matrix form:

where X is the design matrix.

The estimations of the parameters corresponding to matrix βH/A are assessed by Eq. (7):

where X´ is the transpose of matrix X.

The terms X´X y X´YOM/TN corresponding to Eq. (7) are developed in Eqs. (8) and (9):

− − β β β β β

ϵ σ …

β

⋮

⋮ ⋮ ⋮ ⋮ ⋮

β

β

⋮β

⋮

β X′X − ′

′



Each of the coefficients βi,H/A represents the effect of the independent variable on the dependent variable. The estimated value indicates the variation that the dependent variable experiments when the independent variable varies in one unit and the rest of them keep constant.

Having obtained the functions that relate the removal of organic matter and total nitrogen to the HRT, XT, T and So for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb, the coefficient of determination (R2) was evaluated in order to obtain a measurement regarding the goodness of fit, defined as indicated in Eq. (10):

Therefore, for each of the three systems, two functions were obtained to describe the performance of these systems concerning the removal of organic matter and total nitrogen removal as a function of the HRT, XT, T and So. These functions were optimized by analyzing the common operation ranges of HRT (9.5 – 30.4 h), XT (2,798.05 – 3,768.44 mg L-1), T (14.9 – 23.3 ºC), CODinfluent (257.47 – 437.73 mg O2 L-1) and TNinfluent (95.48 – 147.76 mg N L-1) for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb (Tab. S1, Supporting Information).

The optimization was carried out by the Solver add-in facility of Microsoft Office Excel. This software allowed to determine the values of HRT, XT, T and So that maximized the efficiencies regarding organic matter and total nitrogen removal for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb.

Regarding the assessment of the yields of organic matter and total nitrogen removal, the heterotrophic and autotrophic kinetic performances were analyzed by considering the data provided for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb in Tab. S1 and Tab. S2 in the Supporting Information. For this, functions that related the kinetic parameters µm, KS and Y to the operational variables HRT, XT, T and So were proposed by analyzing the mass balances applied to the biological reactor of the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb, according to Text S4 in the Supporting Information. It should be highlighted that the operational variable HRT was related to the sludge retention time (SRT) through Eq. (9) corresponding to Text S4 in the Supporting Information. Thus, the different models could also be expressed as a function of SRT.

In light of this, the following functions, Eqs. (11) – (13), are formulated to establish the relation of the dependent variables, µm, KS y Y, to the independent variables, HRT, XT, T and So:

′

−

−

μλ λ

λ −λ

λ

β i,H/A



The empirical values of µm, KS y Y for the heterotrophic (µm,H, KM and YH) and autotrophic (µm,A, KNH

and YA) biomass can be observed in Tab. S2 in the Supporting Information. The theoretical values of these kinetic parameters were evaluated by considering Eqs. (11) – (13) and the best-fit parameter values (λ1,H/A, λ2,H/A, λ3,H/A, λ4,H/A and λ5,H/A for Eq. (11), φ1,H/A, φ2,H/A, φ3,H/A, φ4,H/A and φ5,H/A for Eq. (12) and α1,H/A, α2,H/A, α3,H/A, α4,H/A and α5,H/A for Eq. (13)) were determined by using the Solver add-in facility of Microsoft Office Excel. In this regard, an objective function was defined as the weighted sum of squares of differences between the empirical and theoretical values and this function was minimized to yield the most appropriate parameters for the considered functions. The values of R2 were calculated according to Eq. (10).

The optimum values of µm,H, µm,A, KM, KNH, YH and YA were assessed by considering the optimum operational conditions of HRT, XT, T and So for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb. Finally, the values of substrate degradation rate for organic matter removal (rsu,H) and substrate degradation rate for total nitrogen removal (rsu,A) were determined to corroborate that were in the operational range for each of the systems analyzed.

3. Results and discussion

3.1. Modeling and optimization of the process of organic matter removal It should be noted that the efficiency of organic matter removal usually decreased when the HRT was lower for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb (Tab. S2, Supporting Information). This occurred as the organic loading rate was higher. Moreover, the increase of biomass concentration did not usually improve the COD removal (Tab. S2, Supporting Information). It could be due to a higher localized competition between the suspended and attached biomass, which could cause an inhibitory effect on the COD removal [25].

The results of the multivariable statistical analysis for organic matter removal are shown in Fig. 1. This analysis shows three triplot diagrams for the MBR (Fig. 1a), hybrid MBBR-MBRa (Fig. 1b) and hybrid MBBR-MBRb (Fig. 1c).

Figure 1

In general, the HRT presented a positive correlation with the COD removal and the kinetic parameters for heterotrophic biomass. It supported the fact that the efficiency of COD removal increased when the HRT was higher.

Regarding the biomass concentration, it should be noted that the MLSS and BD have almost no influence on the COD removal and the kinetic parameters for heterotrophic biomass as the angles between these vectors are of approximately 90º. This explained that the highest biomass concentrations did not usually improve the COD removal. However, the BD showed a positive correlation with the COD removal and heterotrophic kinetic parameters in the hybrid MBBR-MBRb and the length of the BD vector was higher than in the case of the MLSS vector. Therefore, the attached biomass had a higher influence on the COD removal and kinetic parameters for heterotrophic biomass in the hybrid MBBR-MBRb; it could support the highest performance of COD removal under the HRTs of 9.5 h and 6 h in this system, as previously indicated.

φ φ φ −φ φ

α α α −α α



The T did not practically affect the different systems studied regarding the organic matter removal (the angles were of approximately 90º) as its effect was decreased due to the fact that the WWTPs were not outside, but inside a laboratory.

Moreover, the COD removal and the kinetic parameters for heterotrophic biomass had a positive correlation in the three systems, so the kinetic study for heterotrophic biomass supported the results of organic matter removal.

The mathematical models, which express YOM as a linear function of the variables HRT, XT, T and CODinfluent, are defined in Tab. 1 through the coefficients β0,H, β1,H, β2,H, β3,H and β4,H for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb.

Table 1

In this regard, the coefficients β1,H are positive and it corroborates the fact that COD removal and HRT are directly proportional. The same occurs with the coefficients β4,H that show the direct proportion between CODinfluent and COD removal. The slight influence of MLSS and BD on the COD removal (Fig. 1) is supported by the coefficients β2,H, which are close to zero. The effect of T was softened, as indicated previously, and it is confirmed by the low values of the coefficients β3,H, with a value of 0.0041 for the hybrid MBBR-MBRb (Tab. 1).

The values of R2 for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb, 0.9359, 0.9996 and 0.8397, respectively (Tab. 1), indicate that the mathematical models proposed show a high goodness of fit for the process of organic matter removal.

In general, the optimum operational conditions regarding HRT, XT, T and CODinfluent for the three systems correspond to the highest value of the common operation interval (30.4 h, 3,768.44 mg L-1, 23.3ºC and 437.73 mg O2 L-1), with the exception of the hybrid MBBR-MBRb that showed an optimum value for XT of 2,798.05 mg L-1 (Tab. 1). This was probably due to the higher effect of BD on the COD removal and heterotrophic kinetic parameters for this system as compared with the MBR and hybrid MBBR-MBRa.

Regarding the mathematical models to fit the heterotrophic kinetics depending on HRT, XT, T and CODinfluent, it should be noted that the values of R2 corresponding to the hybrid MBBR-MBRa and hybrid MBBR-MBRb are higher than those obtained for the MBR (Tab. 1). This could be probably due to the coexistence of suspended and attached biomass in the hybrid MBBR-MBR systems, which could lead to a modification in the goodness of fit of the kinetic parameters.

In relation to the MBR, µm,H and YH showed a positive correlation with HRT and CODinfluent, and KM had a negative correlation with HRT and CODinfluent, which is supported by the fitting parameters λ1,H and λ5,H (positive values), φ1,H and φ5,H (negative values), and α1,H and α5,H (positive values). The influence of XT on the kinetic parameters is softened with values of -0.0007 and 0.0001 for KM and YH, and showing a strongly negative correlation for the µm,H with a value of -53.0178. In general, this was in accordance with the results shown in Fig. 1. As a whole, the effect of T on heterotrophic kinetic parameters is attenuated, as corroborated through the parameters λ3,H, λ4,H, φ3,H, φ4,H, α3,H and α4,H. This explains the values of angles (of approximately 90º) between T and kinetic parameters observed in Fig. 1.

Concerning the hybrid MBBR-MBRa, the mathematical models show high values of R2 for the fitting of the kinetic parameters µm,H, KM and YH as a function of HRT, XT, T and CODinfluent as compared with MBR, with values of 0.9771, 0.9920 and 0.9999, respectively. It should be pointed out that the slight effect of XT and T on the kinetic parameters, observed in Fig. 1, is supported by the values of λ2,H, λ3,H, λ4,H, φ2,H, φ3,H, φ4,H, α2,H, α3,H and α4,H (Tab. 1). Moreover, the kinetic parameters had usually a positive correlation with CODinfluent as when CODinfluent is higher, the gradient of substrate is higher and the µm,H and YH also increase.



The hybrid MBBR-MBRb has also high values of R2 (Tab. 1) and the mathematical functions describing its kinetic behavior were similar to those obtained for hybrid MBBR-MBRa. It should be noted that µm,H had a strongly positive correlation with XT (Tab. 1) due to the effect of BD, as explained previously for Fig. 1.

The optimum values of µm,H, KM and YH were 0.0172 h-1, 5.2388 mg O2 L-1 and 0.3493 mg VSS mg COD-

1, respectively, for the MBR, 0.0032 h-1, 0.5228 mg O2 L-1 and 0.3444 mg VSS mg COD-1, respectively, for the hybrid MBBR-MBRa, and 0.0102 h-1, 5.6219 mg O2 L-1 and 0.2855 mg VSS mg COD-1, respectively, for the hybrid MBBR-MBRb.

The values of rsu,H were determined for each of the operational conditions analyzed in the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb. Furthermore, the value of optimum rsu,H was assessed by considering the optimum operational conditions and the optimum response of the different systems, shown in Tab. 1. In the MBR, rsu,H was within the range of 20.7146 mg O2 L-1 h-1 and 143.6665 mg O2 L-

1 h-1, and the optimum value was 143.0274 mg O2 L-1 h-1 (Tab. S3, Supporting Information). The value of rsu,H varied between 26.4865 mg O2 L-1 h-1 and 114.1320 mg O2 L-1 h-1 in the hybrid MBBR-MBRa, and the optimum value was 27.3662 mg O2 L-1 h-1 (Tab. S3, Supporting Information). The hybrid MBBR-MBRb showed rsu,H values that fluctuated between 8.4726 mg O2 L-1 h-1 and 377.9639 mg O2 L-1 h-1, and the optimum value was 75.1161 mg O2 L-1 h-1 (Tab. S3, Supporting Information). The optimum rsu,H were in the operation ranges of the different systems, which supported the modeling and optimization processes. In light of this, the MBR had the highest rate of organic matter degradation

under optimum operational conditions as compared with the hybrid MBBR-MBR systems.

3.2. Modeling and optimization of the process of total nitrogen removal The efficiency of TN removal generally decreased when the HRT was lower for each WWTP as the ammonium loading rate was higher. Moreover, the higher the biomass concentration was, the higher the efficiency of TN removal was (Tab. S2, Supporting Information).

The results of the multivariable statistical analysis for nitrogen removal are shown in Fig. 2. This analysis shows three triplot diagrams for the MBR (Fig. 2a), hybrid MBBR-MBRa (Fig. 2b) and hybrid MBBR-MBRb (Fig. 2c).

Figure 2

The HRT had usually a positive correlation with the TN removal and the autotrophic kinetic parameters. It was in accordance with the fact that the efficiency of TN removal increased when the HRT was higher.

Regarding the biomass concentration, MLSS did not have any correlation (angle of 90º approximately) with the TN removal and the autotrophic kinetic parameters for the MBR (Fig. 2a). In the case of the hybrid MBBR-MBRa, BD presented a strongly negative correlation with the TN removal and the autotrophic kinetic parameters, although MLSS showed a positive correlation (Fig. 2b). MLSS and BD showed a positive correlation with the TN removal and the autotrophic kinetic parameters for the hybrid MBBR-MBRb (Fig. 2c), which implies that the attached biomass had an influence on the nitrogen removal and the autotrophic kinetics higher than that obtained for the hybrid MBBR-MBRa. This supported the higher TN removal efficiency under the HRTs analyzed for the hybrid MBBR-MBRb.

The T did not affect the different systems studied regarding the TN removal as its influence was attenuated due to the fact that the WWTPs were not out in the open, but they were inside a laboratory. It also occurred in the process of COD removal, as explained previously.

In general, the TN removal and the kinetic parameters for autotrophic biomass had a positive correlation in the three biological systems, so the autotrophic kinetics supported the results of TN removal.



The mathematical models, which describe YTN as a linear function of the variables HRT, XT, T and TNinfluent, are defined in Tab. 2 through the coefficients β0,A, β1,A, β2,A, β3,A and β4,A for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb.

Table 2

The mathematical models for the process of nitrogen removal have a high goodness of fit due to the values of R2 obtained for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb (Tab. 2). Regarding the MBR, TN removal shows a positive correlation with HRT, and a negative correlation with T and TNinfluent (Fig. 2). This is supported by the values of β1,A (positive), β3,A (negative) and β4,A (negative) (Tab. 2). Moreover, β2,A (-0.0005) reveals the slight influence of MLSS on the TN removal as the angle between these vectors is of approximately 90º (Fig. 2).

In relation to the hybrid MBBR-MBRa, TN removal had a positive correlation with HRT, MLSS and T, and a negative correlation with BD and TNinfluent. This is confirmed by the positive values of β1,A for HRT and β3,A for T; the negative value of β2,A could demonstrate that the influence of BD on the TN removal is higher than that exerted by MLSS (Tab. 2) due to the growth of attached biomass on the carriers moving inside the bioreactor.

The coefficients β1,A, β2,A, β3,A and β4,A for the hybrid MBBR-MBRb corroborate that TN removal is directly proportional to HRT, MLSS and BD, and is inversely proportional to T and TNinfluent (Tab. 2).

According to the mathematical models proposed, the optimum value of HRT is 30.4 h for the three systems analyzed. Regarding the biomass concentration, the optimum performance of the hybrid MBBR-MBRb is achieved at high values of XT, and the optimum behavior of the MBR and hybrid MBBR-MBRa is obtained at low values of XT. Moreover, the MBR and hybrid MBBR-MBRb have the optimum performance for low values of T and TNinfluent, and the hybrid MBBR-MBRa has its best efficiency for high T and TNinfluent (Tab. 2).

In general, the values of R2 obtained for the mathematical models fitting the autotrophic kinetics of the hybrid MBBR-MBR systems as a function of HRT, XT, T and TNinfluent are higher than that corresponding to the MBR (Tab. 2). Thus, the goodness of fit is better in the hybrid MBBR-MBR systems, probably due to the coexistence of suspended and attached biomass, as discussed for the heterotrophic kinetics.

The effect of T on the autotrophic kinetic parameters is softened due to the interior installation of the WWTPs (Fig. 2), which is confirmed by the values of λ3,A, λ4,A, φ3,A, φ4,A, α3,A and α4,A for the three systems (Tab. 2). HRT has a higher influence on the µm,A than on the KNH and YA, as confirmed by λ1,A, φ1,A and α1,A (Tab. 2) as the ammonium loading rate is directly related to the µ corresponding to the biomass. In general, the effect of XT on the autotrophic kinetics is attenuated, as indicated by φ2,A and α2,A (Tab. 2), probably due to competitive phenomena between suspended and attached biomass. It should be pointed out that XT has the highest influence on the µm,A for the hybrid MBBR-MBRb as λ2,A

shows the highest value (Tab. 2). This is in accordance with the greatest influence of attached biomass present in the hybrid MBBR-MBRb, which allows to obtain better TN removal efficiency.

In general, it should be noted that KNH and TNinfluent are directly proportional as KNH reaches a constant value at high substrate concentrations according to Monod model.

Regarding the optimum values of µm,A, KNH and YA, they were 0.0304 h-1, 1.0574 mg N L-1 and 0.4067 mg O2 mg N-1, respectively, for the MBR, 0.0208 h-1, 5.2873 mg N L-1 and 1.5912 mg O2 mg N-1, respectively, for the hybrid MBBR-MBRa, and 0.0172 h-1, 0.7384 mg N L-1 and 0.8506 mg O2 mg N-1, respectively, for the hybrid MBBR-MBRb.

The values of rsu,A were also determined for the operational conditions and optimum operational conditions (optimum rsu,A) analyzed in the three systems (Tab. 2). In the MBR, rsu,A was within the range of 40.7476 mg N L-1 h-1 and 368.1191 mg N L-1 h-1, and the optimum value was 64.6223 mg N L-1



h-1 (Tab. S3, Supporting Information). The value of rsu,A varied between 36.6366 mg N L-1 h-1 and 59.7009 mg N L-1 h-1 in the hybrid MBBR-MBRa, and the optimum value was 37.1061 mg N L-1 h-1 (Tab. S3, Supporting Information). The hybrid MBBR-MBRb showed rsu,A values that fluctuated between 31.7557 mg N L-1 h-1 and 98.5505 mg N L-1 h-1, and the optimum value was 42.9504 mg N L-1 h-1 (Tab. S3, Supporting Information). The optimum values of rsu,A were within the operation ranges of the different systems, which supported the modeling and optimization processes. In this regard, the MBR had also the highest rate of total nitrogen removal under optimum operational conditions.

To finish this section, Fig. 3 shows that the type of system, HRT and BD are the main variables which have influence on the performance for the biological processes of COD and TN removal as they had a positive correlation with the organic matter and nitrogen removal and the heterotrophic and autotrophic kinetics of the different bioreactors. Nevertheless, T and MLSS have practically no effect on the response of the system, as discussed previously.

Figure 3

4. Conclusions The organic matter removal (YOM) and total nitrogen removal (YTN) could be modeled depending on hydraulic retention time (HRT), total biomass concentration (XT), temperature (T), and COD of the influent (CODinfluent) for organic matter removal or TN of the influent (TNinfluent) for total nitrogen removal according to the following equation:

Heterotrophic and autotrophic kinetic performance in terms of maximum specific growth rate (µm), half-saturation coefficient (KS) and yield coefficient (Y) could be modeled as a function of HRT, XT, T, and CODinfluent or TNinfluent according to the following equations:

(iii) In general, the values of coefficient of determination (R2) for the different models regarding COD and TN removal and kinetic behavior supported the mathematical modeling and were higher for the hybrid MBBR-MBR systems than those obtained for the MBR. This was probably due to the coexistence of suspended and attached biomass in the hybrid MBBR-MBR systems.

Acknowledgment The authors wish to thank the Ministry of Education, Culture and Sport of Spain for the FPU grant no. AP2010-1552 awarded to J.C. Leyva-Díaz, as well as the University of Granada in the training plan “Programa de Ayudas Puente” and the program “Convocatoria de ayudas a Proyectos de I+D Excelencia 2013” (CTM2013-48154-P).

β β β β β

μλ λ

λ −λ

λ

φ φ φ −φ φ

α α α −α α



Symbols used BD [mg L-1] biofilm density

COD [mg O2 L-1] chemical oxygen demand

CODinfluent [mg O2 L-1] chemical oxygen demand of the influent

HRT [h] hydraulic retention time

KM [mg O2 L-1] half-saturation coefficient for organic matter

KNH [mg N L-1] half-saturation coefficient for ammonia nitrogen

Qo [L h-1] volumetric flow rate of influent

Qs [L h-1] volumetric flow rate of effluent

rsu [mg O2 L-1 h-1] substrate degradation rate

rx [mg VSS L-1 h-1] cell growth rate

So [mg L-1] substrate concentration of influent

Ss [mg L-1] substrate concentration of effluent

T [ºC] temperature

V [L] bioreactor volume

XT [mg L-1] total biomass concentration

YA [mg O2 mg N-1] yield coefficient for autotrophic biomass

YH [mg VSS mg COD-1] yield coefficient for heterotrophic biomass

µm,A [h-1] maximum specific growth rate for autotrophic biomass

µm,H [h-1] maximum specific growth rate for heterotrophic biomass

Abbreviations DCA detrended correspondence analysis

KS substrate half-saturation coefficient

MBBR moving bed biofilm reactor

MBR membrane bioreactor

MBBR-MBR moving bed biofilm reactor-membrane bioreactor

MLSS mixed liquor suspended solids

RDA redundancy analysis

S substrate concentration

TN total nitrogen

TNinfluent total nitrogen of the influent

VSS volatile suspended solids

WWTP wastewater treatment plant

Y yield coefficient



YOM removal of organic matter

YTN removal of total nitrogen

µ specific growth rate

µm maximum specific growth rate

References [1] P. Chave, The EU Water Framework Directive: An Introduction, IWA Publishing, London 2001.

[2] A. A. L. Zinatizadeh, E. Ghaytooli, J. Taiwan Inst. Chem. Eng. 2015, 53, 98-111. DOI: 10.1016/j.jtice.2015.02.034.

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[9] J. C. Leyva-Díaz, K. Calderón, F. A. Rodríguez, J. González-López, E. Hontoria, J. M. Poyatos, Biochem. Eng. J. 2013, 77, 28-40. DOI: 10.1016/j.bej.2013.04.023.

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[11] S. Judd, C. Judd, The MBR Book. Principles and Applications of Membrane Bioreactors for Water and Wastewater Treatment, 2nd ed., Elsevier, Amsterdam 2011.

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[15] Y. Qiqi, H. Qiang, H. T. Ibrahim, Pak. J. Nutr. 2012, 11 (9), 804-811. DOI: 10.3923/pjn.2012.804.811.

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[17] M. Henze, W. Gujer, T. Mino, M. van Loosdrecht, Activated sludge models ASM1, ASM2, ASM2d and ASM3, IWA Task Group on mathematical modelling for design and operation of biological wastewater treatment, in: IWA Scientific and Technical Report No. 9, 2000.

[18] I. Iacopozzi, V. Innocenti, S. Marsili-Libelli, E. Giusti, Environ. Modell. Softw. 2007, 22, 847-861. DOI: 10.1016/j.envsoft.2006.05.009.



[19] A. Rivas, I. Irizar, E. Ayesa, Environ. Modell. Softw. 2008, 23, 435-450. DOI: 10.1016/j.envsoft.2007.06.009.

[20] D. C. Montgomery, G. C. Runger, N. F. Hubele, Engineering Statistics, 2nd ed., John Wiley & Sons, New Jersey 2001.

[21] D. C. Montgomery, G. C. Runger, Probabilidad y estadística aplicadas a la ingeniería, 2nd ed., Limusa Wiley, Mexico City 2012.

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[23] M. J. K. Bashir, S. S. Abu Amr, S. Q. Aziz, N. C. Aun, S. Sethupathi, Middle East J. Sci. Res. 2015, 23 (2), 244-252. DOI: 10.5829/idosi.mejsr.2015.23.02.52.

[24] J. Lepš, P. Šmilauer, Multivariate analysis of ecological data using CANOCO, Cambridge University Press, Cambridge 2003.

[25] S. Okabe, Y. Oozawa, K. Hirata, Y. Watanabe, Water Res. 1996, 30, 1563-1572. DOI: 10.1016/0043-1354(95)00321-5.



Tables Table 1. Mathematical modeling of the organic matter removal and heterotrophic kinetics and optimization of the operational conditions, organic matter removal and heterotrophic kinetic parameters for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb

Parameter Wastewater treatment plant

MBR Hybrid MBBR-MBRa Hybrid MBBR-MBRb

Organic matter removal

β0,H 75.4417 78.4221 83.5976

β1,H 0.1324 0.1207 0.2101

β2,H 0.0004 0.0004 -0.0001

β3,H 0.1622 0.1587 0.0041

β4,H 0.0211 0.0129 0.0062

R2 0.9359 0.9996 0.8397

Optimum operational conditions

HRT (h) 30.4 30.4 30.4

XT (mg L-1) 3,768.44 3,768.44 2,798.05

T (ºC) 23.3 23.3 23.3

CODinfluent (mg O2 L-1) 437.73 437.73 437.73

Heterotrophic kinetics

λ1,H 0.1469 0.2521 0.5598

λ2,H -53.0178 2.0012 -137.3317

λ3,H -0.0001 -0.0084 -0.0001

λ4,H -86.2743 2.0385 -95.5619

λ5,H 0.0001 0.0001 0.0001

R2 0.5317 0.9771 0.8962

φ1,H -0.4230 0.1138 -0.4716

φ2,H -0.0007 -0.0053 -0.0002

φ3,H 27.2068 6,350.3586 51.8616

φ4,H 1.1901 208,282.3455 21.9409

φ5,H -2,277.9237 7,482.2212 105.0190

R2 0.3266 0.9920 0.8225

α1,H 0.0027 -0.0030 -0.0081

α2,H 0.0001 0.0001 0.0001

α3,H -1.2502 0.0956 0.3017

α4,H 70.9638 -21.0289 -3.8492

α5,H 102.8386 22.9032 25.8231

R2 0.6810 0.9999 0.9960

Optimum response

YOM (%) 93.96 92.86 92.44

µm,H (h-1) 0.0172 0.0032 0.0102

KM (mg O2 L-1) 5.2388 0.5228 5.6219

YH (mg VSS mg COD-1) 0.3493 0.3444 0.2855



Table 2. Mathematical modeling of the total nitrogen removal and autotrophic kinetics and optimization of the operational conditions, total nitrogen removal and autotrophic kinetic parameters for the MBR, hybrid MBBR-MBRa and hybrid MBBR-MBRb

Parameter Wastewater treatment plant

MBR Hybrid MBBR-MBRa Hybrid MBBR-MBRb

Total nitrogen removal

β0,A 91.6386 9.2995 55.9449

β1,A 1.0587 0.0707 0.7128

β2,A -0.0005 -0.0004 0.0036

β3,A -1.1248 1.3679 -0.6312

β4,A -0.2630 0.2290 -0.0778

R2 0.6292 0.9998 0.8785

Optimum operational conditions

HRT (h) 30.4 30.4 30.4

XT (mg L-1) 2,798.05 2,798.05 3,768.44

T (ºC) 14.9 23.3 14.9

TNinfluent (mg N L-1) 95.48 147.76 95.48

Autotrophic kinetics

λ1,A 2.3048 -0.0200 1.3454

λ2,A -28.0609 -1.9999 80.5271

λ3,A -0.1376 0.1923 -0.0140

λ4,A -0.3194 -1.1025 -16.8966

λ5,A 0.0011 -0.0012 -0.0001

R2 0.6034 0.9999 0.9202

φ1,A 0.0312 -0.0162 -0.0005

φ2,A 0.0001 0.0004 -0.0005

φ3,A 2,646,946,350 2,646,946,350 12.5407

φ4,A 443.4123 468.7242 22.8494

φ5,A -8.1052 -8.2148 6.9145

R2 0.9727 0.9999 0.8501

α1,A -0.0611 -0.0298 -0.0221

α2,A 0.0002 -0.0001 0.0001

α3,A 1.3030 5.3847 53.8562

α4,A -4.1793 15.8346 86.0659

α5,A 2.5460 -0.8288 82.7301

R2 0.6235 0.9999 0.9384

Optimum response

YTN (%) 80.46 75.94 74.35

µm,A (h-1) 0.0304 0.0208 0.0172

KNH (mg N L-1) 1.0574 5.2873 0.7384

YA (mg O2 mg N-1) 0.4067 1.5912 0.8506



Figure legends

Figure 1. Triplot diagram for RDA of the kinetic parameters for heterotrophic biomass, μm,H, KM, YH, and COD removal (Tab. S2, Supporting Information) in relation to the variables HRT, MLSS, BD, T and CODinfluent (Tab. S1, Supporting Information) in the MBR (a), hybrid MBBR-MBRa (b) and hybrid MBBR-MBRb (c).

-1.0 1.0

-1.0

1.0

KM

kdHRT

MLSST

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remoMumH

KM

YH kdHRT

MLSS

BD

TCOD infl

MLSST

HRT

COD influent

kd

COD removal

-1.5 1.5

-1.0

1.0

COD remoMumH

KMYH

kd

HRT

MLSS

BD

T

COD infl

MLSS

BD

T HRT

COD influent

COD removal

KM YH

kd μm, H

(b)

(a)

MLSS T

COD influent

HRT

COD removal

KM kd

-1.0 1.0

-1.0

1.0

COD remo

MumHKMYH

kdHRT

MLSST

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remoMumH

KM

YH kdHRT

MLSS

BD

TCOD infl

MLSST

HRT

COD influent

YH

kd μm, H

COD removal

KM

-1.5 1.5

-1.0

1.0

COD remoMumH

KMYH

kd

HRT

MLSS

BD

T

COD infl

MLSS

BD

T HRT

COD influent

COD removal

KM YH

kd μm, H

(b)

(a)

MLSS

COD influent

HRT T

BD

KM YH

COD removal μm, H

kd

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remo

MumH

KM

YH

kd HRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD

remo

MumH

KM

YHkdHR

T

MLSS

BD

T

COD

infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

COD influent

HRT

BD T

MLSS

KM

COD removal

kd

μm, H YH

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD inflCOD influent

HRT

MLSS

T

BD

kd

COD removal

KM

YH μm, H

(a)

(b)

COD influent

MLSS

T BD

COD removal

KM kd HRT

YH μm, H

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5-1

.0

1.0

COD remo

MumH

KM

YH

kd HRT

MLSS

BD

T

COD infl

-1.5 1.5-1

.01.

0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD

remo

MumH

KM

YHkdHR

T

MLSS

BD

T

COD

infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

COD influent

HRT

BD T

MLSS

KM

COD removal

kd

μm, H YH

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T


HRT

MLSS

T

BD

kd

COD removal

KM

YH μm, H

(a)

(b)

COD influent

KM

T

MLSS

BD

COD removal

kd

μm, H YH

[Escriba una cita del documento o el resumen de un punto interesante. Puede situar el cuadro de texto en cualquier lugar del documento. Use la ficha Herramientas de dibujo para cambiar el formato del cuadro de texto de la cita.]

(c) (d)

(b)

(a)

YH

KM dd kd μm, H

KM YH kd μm, H

COD removal

COD removal

KM

COD removal

kd

μm, H YH

KM kd

COD removal

μm, H YH

BD

-1.0 1.0

-1.0

1.0

COD remo

MumHKMYH

kdHRT

MLSST

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0COD remo

MumH

KM

YH kdHRT

MLSS

BD

TCOD infl

MLSST

HRT

COD influent

YH

kd μm, H

COD removal

KM

-1.5 1.5

-1.0

1.0

COD remoMumH

KMYH

kd

HRT

MLSS

BD

T

COD infl

MLSS

BD

T HRT

COD influent

COD removal

KM YH

kd μm, H

(b)

(a)

MLSS T

COD influent

HRT

COD removal

KM

YH

kd μm, H

-1.0 1.0

-1.0

1.0

COD remo

MumHKMYH

kdHRT

MLSST

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remoMumH

KM

YH kdHRT

MLSS

BD

TCOD infl

MLSST

HRT

COD influent

YH

kd μm, H

COD removal

KM

-1.5 1.5

-1.0

1.0

COD remoMumH

HRT

MLSS

BD

T

COD infl

MLSS

BD

T HRT

COD influent

COD removal

μm, H

(b)

(a)

MLSS

COD influent

HRT T

BD

COD removal μm, H

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remo

MumH

KM

YH

kd HRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD

remo

MumH

KM

YHkdHR

T

MLSS

BD

T

COD

infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

COD influent

HRT

BD T

MLSS

KM

COD removal

kd

μm, H YH

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T


HRT

MLSS

T

BD

kd

COD removal

KM

YH μm, H

(a)

(b)

COD influent

MLSS

T BD

COD removal

KM kd HRT

YH μm, H

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remo

MumH

KM

YH

kd HRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5-1.0

1.0

COD

remo

MumH

KM

YHkdHR

T

MLSS

BD

T

COD

infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

COD influent

HRT

BD T

MLSS

KM

COD removal

kd

μm, H YH

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T


HRT

MLSS

T

BD

kd

COD removal

KM

YH μm, H

(a)

(b)

COD influent

KM

T

MLSS

BD

COD removal

kd

μm, H YH


(c) (d)

(b)

(a)

YH

KM kd μm, H

KM YH

μm, H

COD removal

COD removal

KM

COD removal

kd

μm, H YH

KM kd

COD removal

μm, H YH

BD

-1.0 1.0

-1.0

1.0

COD remo

MumHKMYH

kdHRT

MLSST

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remoMumH

KM

YH kdHRT

MLSS

BD

TCOD infl

MLSST

HRT

COD influent

YH

kd μm, H

COD removal

KM

-1.5 1.5

-1.0

1.0

COD remoMumH

KMYH

kd

HRT

MLSS

BD

T

COD infl

MLSS

BD

T HRT

COD influent

COD removal

KM YH

kd μm, H

(b)

(a)

MLSS T

COD influent

HRT

COD removal

KM

YH

kd μm, H

-1.0 1.0

-1.0

1.0

COD remo

MumHKMYH

kdHRT

MLSST

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remoMumH

KM

YH kdHRT

MLSS

BD

TCOD infl

MLSST

HRT

COD influent

YH

kd μm, H

COD removal

KM

-1.5 1.5

-1.0

1.0

COD remoMumH

KMYH

kd

HRT

MLSS

BD

T

COD infl

MLSS

BD

T HRT

COD influent

COD removal

KM YH

kd μm, H

(b)

(a)

MLSS

COD influent

HRT T

BD

KM YH

COD removal μm, H

kd

-1.5 1.5

-1.0

1.0

COD remo

MumH YH

MLSS

BD

T

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remo

MumH

KM

YH

kd HRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0CO

D rem

o

MumH

KM

YHkdHR

T

MLSS

BD

T

COD

infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

BD T

MLSS

COD removal

μm, H YH

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T


HRT

MLSS

T

BD

kd

COD removal

KM

YH μm, H

(a)

(b)

COD influent

MLSS

T BD

COD removal

HRT

YH μm, H

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD remo

MumH

KM

YH

kd HRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.5

1.5

-1.0

1.0

COD

remo

MumH

KM

YHkdHR

T

MLSS

BD

T

COD

infl

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

COD influent

HRT

BD T

MLSS

KM

COD removal

kd

μm, H YH

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T


HRT

MLSS

T

BD

kd

COD removal

KM

YH μm, H

(a)

(b)

COD influent

KM

T

MLSS

BD

COD removal

kd

μm, H YH


(c) (d)

(b)

(a)

YH

KM kd μm, H

KM YH kd μm, H

COD removal

COD removal

KM

COD removal

kd

μm, H YH

KM kd

COD removal

μm, H YH

BD



Figure 2. Triplot diagram for RDA of the kinetic parameters for autotrophic biomass, μm,A, KNH, YA, and TN removal (Tab. S2, Supporting Information) in relation to the variables HRT, MLSS, BD, T and TNinfluent (Tab. S1, Supporting Information) in the MBR (a), hybrid MBBR-MBRa (b) and hybrid MBBR-MBRb (c).

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS T

TN influent

HRT

YA

KNH

μm, A

TN removal

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS

BD

TN influent

HRT

T

μm, A

TN removal

YA

KNH

(b)

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0-1

.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN removM

umA

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a)

(d) MLSS

TN influent

BD

T KNH

μm, A

HRT TN removal

YA

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN remov

Mum

A

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a) (c)

MLSS

BD

T YA

KNH

TN influent

μm, A

TN removal HRT

(a)

(d) (c)

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS T

TN influent

HRT

YA

KNH

μm, A

TN removal

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS

BD

TN influent

HRT

T

μm, A

TN removal

YA

KNH

(b)

-1.0 1.0-0

.61.

0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN removM

umA

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a)

(d) MLSS

TN influent

BD

T KNH

μm, A

HRT TN removal

YA

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN remov

Mum

A

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a) (c)

MLSS

BD

T YA

KNH

TN influent

μm, A

TN removal HRT

(a)

(d) (c)

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS T

TN influent

HRT

YA

KNH

μm, A

TN removal

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS

BD

TN influent

HRT

T

μm, A

TN removal

YA

KNH

(b)

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN removM

umA

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a)

(d) MLSS

TN influent

BD

T KNH

μm, A

HRT TN removal

YA

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN remov

Mum

A

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a) (c)

MLSS

BD

T YA

KNH

TN influent

μm, A

TN removal HRT

(a)

(d) (c)

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS T

TN influent

HRT

YA

KNH

μm, A

TN removal

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS

BD

TN influent

HRT

T

μm, A

TN removal

YA

KNH

(b)

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN removM

umA

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a)

(d) MLSS

TN influent

BD

T KNH

μm, A

HRT TN removal

YA

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN remov

Mum

A

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a) (c)

MLSS

BD

T YA

KNH

TN influent

μm, A

TN removal HRT

(a)

(d) (c)

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS T

TN influent

HRT

YA

KNH

μm, A

TN removal

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS

BD

TN influent

HRT

T

μm, A

TN removal

YA

KNH

(b)

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN removM

umA

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a)

(d) MLSS

TN influent

BD

T KNH

μm, A

HRT TN removal

YA

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

TN influ

MLSS

BD

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN remov

Mum

A

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a) (c)

MLSS

BD

T YA

KNH

TN influent

μm, A

TN removalremovalremovalTN removal HRT

(a)

(d) (c)

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS T

TN influent

HRT

YA

KNH

μm, A

TN removal

Hybrid -1.0 1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm, A

KNH

T

TN influent

HRT

-1.0

1.0

-1.0

1.0

TN remov

MumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal

μm

, A

KNH

T

TN influent

HRT

T

-1.0

1.0

-1.0

1.0

TN re

mov MumA

KNH

YA

HRT

MLSS

T

TN in

flu

MLSS

YA

TN remov

al

μm, A

KNH T

TN influ

ent

HRT

HRT

-1.5 1.5

-1.5

1.0

TN remov

MumAKNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

T

BD

TN influent

μm, A

TN removal

KNH

YA

HRT

HRT TN influent

T

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μ

m, A

KNH

T

TN influent

HRT

MLSS (b)

(a)

MLSS

BD

TN influent

HRT

T

μm, A

TN removal

YA

KNH

(b)

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN removM

umA

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a)

(d) MLSS

TN influent

BD

T KNH

μm, A

HRT TN removal

YA

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

MLSS

BD

T

HRT

YA

KNH

TN removal

μm, A

TN influent

-1.0

1.0

-1.0

1.0

TN removMumA

KNH

YA

HRT

MLSS

T

TN influ

MLSS

YA

TN removal μm, A

KNH

T

TN influent

HRT

TN influent

T

MLSS

BD

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.0

1.0

-0.6

1.0

TN remov

Mum

A

KNH

YA

HRT

MLSS

BD

T

TN influ

YA

-1.0

1.0

-0.6

1.0

TN re

mov

Mum

A

KNH

YA

HRT

MLS

SB

D

T

TN in

flu

-1.0 1.0

-0.6

1.0

TN removMumA

KNH

YA

HRT

MLSS

BD

T

TN influ

-1.5 1.5

-1.0

1.0

COD remo

MumH

KM

YH

kdHRT

MLSS

BD

T

COD infl

MLSS

T

HRTTN removal

μm, A

BD

TN influent YA KNH

T

TN influent

(b)

(a) (c)

MLSS

BD

T YA

KNH

TN influent

μm, A

TN removal HRT

(a)

(d) (c)



Figure 3. Triplot diagram for RDA of the COD and TN removal, heterotrophic and autotrophic kinetic parameters, μm,H, KM, YH, μm,A, KNH, YA, in relation to the variables: wastewater treatment technology (system), HRT, MLSS, BD and T.

-1.0 1.0

-1.0

1.0

COD remoMumH

KM

YH

TN remov

KNH

YA

kd

HRT

SYSTEM

MLSS

BD

-1.0

1.0

-1.0

1.0

COD remo

MumH

KM

YH

TN remov

MumA

KNH

YA

kd

HRT

SYSTEM

MLSS

BD

-1.0 1.0

-1.0

1.0

COD remoMumH

KM

YH

TN remov

MumA

KNH

YA

kd

HRT

SYSTEM

MLSS

BD

-1.0 1.0

-1.0

1.0

COD remoMumH

KM

YH

TN remov

MumA

KNH

YA

kd

HRT

SYSTEM

MLSS

BDSYSTEM

BD

TN removal YA

, A

HRTHRTHRTMLSS

KNH

KM

μm, H kd

YH

COD removal

T



Table of contents The aim of this study was to develop mathematical models in terms of organic matter and nitrogen removal and kinetic performance to optimize the operation conditions. The operation conditions were the hydraulic retention time, total biomass concentration, temperature and chemical oxygen demand of the influent or total nitrogen of the influent.

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